 So, we will talk about a very important instrument in this chapter, which is called moving coil galvanometer. We just first check the construction of it, the magnetic field will be like this and then there is a pointer attached with this drum, first draw this and that, see if this in this construction, what is there, there is a north pole and there is a south pole and you have wrapped the coil around this cylinder, this cylinder is flew to rotate about this axis, so it can just rotate like this and this coil is wrapped in such a way that the magnetic field is always perpendicular to the coil, now if I pass some current in this coil, if I pass a current in this coil, will it have any magnetic moment, what is magnetic moment Kevin? It has a magnetic moment or not, it has a magnetic moment and it is kept in a magnetic field, so will it have a torque, how much is the torque? Torque is m cross b, fine torque is m cross b, so if I put a current in this coil, this entire drum will rotate and if this drum rotates, the pointer will move, getting it, if you pass a small current and if you pass a bigger current, what will be the difference in the rotation, if you pass a small current till when it will rotate or will it stop after some time, it will keep on rotating, it will keep on rotating, right, because the magnetic moment is always perpendicular to the magnetic field, so it will keep on experiencing torque, it will just keep on rotating, fine, but then if you pass a larger current, what is the difference between rotation due to a larger current and rotation due to a smaller current, it quicker, angular acceleration will be more, when the current is more, angular acceleration will be more, fine, so basically this pointer will swing all the way in both, you cannot calculate the angular acceleration while looking at it and determine how much is the current, fine, so it becomes difficult to check using this right now as in how much is the current, fine, so you have to do something else, right, so what you do here is, you put a torsional spring over here, like this, have you seen that the toys, they will have a spring like this, when you put the key, when you rotate the key, it just wraps around, like this, have you seen this, right, so when you leave it, it tries to go back to its original shape like what every spring does and when it tries to go here, it rotates, fine, this torsional spring will create torque, it will not create force, it tries to open up, are you getting this point, okay, so just like a linear spring will have force is equal to k times x, a torsional spring will have torque is equal to k times eta, some spring constant k into theta, depending on how stiff the spring is, the spring constant k will vary for the torsional spring, getting it, and more you rotate, more you rotate, more is the resistance torque, right, when you put the key in the toy, initially it will be easy then become more difficult because the angular rotation increases, right, so similar kind of spring is attached here, one end of the spring is on the moving cylinder, rotating cylinder and the other end of the spring is fixed on this galvanometer, this is a galvanometer, the other end is on the structure of galvanometer, getting it, so when this cylinder rotates, only it takes this point and rotates, getting it or you can put this on cylinder and this on the structure because this point at the center will not even move actually, fine, so this point will rotate with the cylinder and this point is on the structure, so what will happen when this moves, the spring will get, right, and because of that spring will create a torque, fine, so this coil which has a current, that coil is also experiencing a torque, right, because of its rendering experiencing torque, but what torque spring is providing is the resistance against the rotation, spring will oppose any movement from its natural shape and size, fine, so this when it rotates, the spring gets distorted, so spring will try to come back to its original, getting it, now when this will stop, this pointer will stop when torque on this become equal to torque on the spring, getting it, get it out, no, no, right, so how much is a torque on this coil if number of turns is n and area is a, current is i, how much is the torque on the coil, torque on the coil due to magnetic field, how much, how much it is, m cross b is the torque, right, m is what n i a, this cross with the b and the magnetic moment, they are 90 degree to each other, so this is the torque, fine, and torque on the spring is what, spring constant times theta, fine, so when these two become equal, the cylinder will stop rotating, theta is equal to n a b, so this by k times, what is theta, the amount of rotation, fine, so depending on the current, what is the current, theta will be different for different currents, right, and what is this, this is what number of turns in the coil that is the inside the instrument, a is area of the coil again inside the instrument, b is what, magnetic field, this magnet is inside the instrument, k is spring again inside the instrument, so this entire thing, the bracket term is called gallium meter constant, because this thing depends on what gallium meter you are using, everything is inside, so now if you know the gallium meter constant and you know how much this thing has rotated, you will exactly know what is the current, getting it, right, so you need a torsional spring to stop it, so that you will able to estimate what is the current, do you know this gallium meter is a very very sensitive instrument, have you seen this gallium meter in your lab, what you have used it for, which experiment, where have you used gallium meter, cell and how you calculate it, potential meter, right, so you find a null point, have you ever measured the current using gallium meter, you measured it or you just detected it, you just detected the current using gallium meter, so gallium meter is a very very sensitive instrument, that is used to detect whether there is a current or not, the bigger current you will not have, if the current is high, you will not be like confused about it, but if current is very less, you will try to find out exactly where it is 0, so like in potential meter where you have to find the null point, it is used, and there are other instruments also where the null point is important, where you use gallium meter, but then if you want to use gallium meter as emitter, you want to actually measure the current using gallium meter, what will happen in gallium meter, there will be a scale in gallium meter also, but the scale will be very very less, like from 0 to 10 milli ampere, but then suppose you want to increase the scale, you want to measure up to 2 ampere, fine, the gallium meter shows the full deflection for just 10 milli ampere, this is 10 milli ampere, fine, so if you pass a current more than 10 milli ampere, what will happen, there is a stopper here, it won't go beyond that, so basically what is happening, you are not able to measure beyond 10 milli ampere, because the scale itself stops at 10 milli ampere, fine, and suppose you want to measure 2 ampere, then what should happen, no, you want, you want to, you are filled to modify it, no, you can't open up the gallium meter, how to, tell me the reason, don't just remember the stuff and how, I mean what all things are required, if 10 milli ampere, beyond 10 milli ampere you are not able to measure, you want to measure 2 ampere, so what is the thing which you require, you are not understanding what I am asking you is, suppose you want to measure 2 milli ampere, fine, if you pass 1.5 milli ampere, what should happen, should it show full deflection, it should be in between somewhere, isn't it, so current less than 2 milli ampere should be less than full deflection, that is required, 2 ampere can show the full deflection, so full deflection means 2 ampere, then, are you getting it, so you want to do that, one thing is as he said, increase the scale length, so how much you increase it, you will make it full circle also, then it also will not become so empty, are you getting it, or you increase, see this, this doesn't matter, you are not understanding the thing here, this you can shrink it to 2 kilometer also, but the angle of rotation will be, let me mind by what is the current, fine, it will still, if you show that, this is 2 kilometer now, and this is 0 kilometer, it will still show 2 kilometer for 10 milli ampere, are you getting it, so just changing the scale will not help you, fine, so we have to do something else, but one thing is pretty sure, that if 10 milli ampere current goes inside the gallonometer, it will show full deflection, fine, so you have to do a construction in which the 2 ampere might be coming from outside, but you just allow 10 milli ampere inside the gallonometer, rest of it should be bypassed, are you getting the point, fine, so basically externally you are seeing that 2 milli ampere is coming, but your circuit should be such that if 2 ampere comes, 10 milli ampere goes to gallonometer, if 1.5 ampere comes, only less than 10 milli ampere goes to the gallonometer, getting it, so for converting gallonometer into emitter of 2 ampere, it should show full deflection for 2 ampere, right, so you connect a small resistance in parallel, a gallonometer is shown like this, this is a gallonometer with its own resistance, let us call it as RG, this is the complete gallonometer, okay, brought this, everything has a resistance, so this is like yeah, internal resistance, suppose you want to measure a current I, okay, so gallonometer shows full deflection for IG only, getting it, what should be the value of small R for gallonometer to measure up to current capital R, kind of.